If `a ,\ b ,\ c ,\ d\ a n d\ p` are different real numbers such that: `(a^2+b^2+c^2)p^(2)-2(a b+b c+c d)p+(b^2+c^2+d^2)lt=0` , then show that `a ,\ b ,\ c` and `d` are in G.P.

Explanation

Given `(a^2 + b^2 + c^2)p^2 – 2(ab + bc + cd)p + (b^2 + c^2 + d^2) le 0 `


`(a^2 + b^2 + c^2)p^2 – (2abp + 2bcp + 2cdp) + (b^2 + c^2 + d^2) le 0 `


`(ap -b)^2 + (bp – c)^2 + (cp – d)^2 le 0`


Sum of squares cannot be negative.


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